International Journal of Theoretical Physics

, Volume 46, Issue 11, pp 2887–2900 | Cite as

An Intrinsic Topology for Orthomodular Lattices



We present a general way to define a topology on orthomodular lattices. We show that in the case of a Hilbert lattice, this topology is equivalent to that induced by the metrics of the corresponding Hilbert space. Moreover, we show that in the case of a boolean algebra, the obtained topology is the discrete one. Thus, our construction provides a general tool for studying orthomodular lattices but also a way to distinguish classical and quantum logics.


Hilbert Space Modal Logic Boolean Algebra Closed Subspace Quantum Logic 
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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Leibniz-IMAG LaboratoryGrenobleFrance

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